Generally receivers are well known and widely used particularly in wireless communications systems such as certain selective messaging systems. Many current selective message systems employ digital modulation techniques to facilitate conveyance of information over the communication media or channel. This together with more capable digital signal processors (DSPs) have popularized various digital processing techniques now used by practitioners to perform various receiver or system sub-functions, such as timing or frequency synchronization or symbol recovery associated with receiving information. In particular recovery of digital modulation normally requires that the receiving end or receiver of a message have a timing reference or clock that is closely aligned with the clock or timing reference at the transmitting end.
Often practitioners resort to sampled data receivers where the incoming signal is digitized and thereafter, using DSPs, digitally processed to eventually yield a detected symbol. This digital processing may be very complex and practitioner routinely search for more efficient approaches for digital processing. For example symbol recovery may well require some form of Fourier Transform or more specifically some form of Fourier transform suitable for sampled data. Such Fourier transforms include a discrete time Fourier transform (DTFT) that exists for any frequencies less that the sampling frequency and the discrete Fourier transform (DFT) which exists only at N discrete equally spaced frequencies where N is the number of samples used to determine the DFT. A fast Fourier transform (FFT) is a fast or efficient algorithm for finding a DFT and is one known approach for limiting processing resource requirements.
Various relatively well known approaches exist to determine the DTFT or DFT. Which transform is needed will depend on the requisites for the transform. For example to find a Fourier transform at an arbitrary frequency requires a DTFT as it is the only one of the above transforms that exists for all frequencies. This is unfortunate as the known DTFT approaches are relatively calculation intensive and therefore may require relatively capable DSPs or the like. This capability entails significant disadvantages such as processor costs or calculation time and power consumption which may be an issue in portable receiver applications. Further known approaches for determining a DTFT may require a processor with extended dynamic range further exasperating the economic burdens. Similarly determining an accurate timing reference may be a complex processing task, requiring, for example, the calculation of a correlation or cross correlation. Because of the complexity involved and limited processing resources practitioners have not used a correlation for timing error detection or timing acquisition, choosing instead some less processing intensive approach that may be less accurate. At higher symbol speeds this lack of accuracy and the resultant reduction in receiver sensitivity becomes much more of a problem. For these reasons timing recovery or error detection has tended to be less accurate or more complex than is ordinarily desirable. Clearly a need exists for an apparatus and method for timing recovery or timing error detection in a receiver that is accurate and processing resource efficient.